2'4 Signed integer representation 2'6 Character codes

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2.4 Signed integer representation2.6
Character codes

• Nguyen Le
• CS147

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Section overview

• 2.4 Signed Integer Representation
• 2.4.1 Signed Magnitude
• 2.4.2 Complement Systems
• 2.4.3 Unsigned Versus Signed Numbers
• 2.4.4 Computers, Arithmetic, and Booths
  Algorithm
• 2.4.5 Carry Versus Overflow

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Unsigned integer representation

• 1 1 1 1 ? carries
• 0 1 0 1 1 1 0 0
• 0 1 1 0 1 0 1 1
• 1 1 0 0 0 1 1 1

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3 methods of representation

• Signed magnitude
• Ones complement
• Twos complement

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Signed magnitude

• Signed magnitude representation includes a sign
  as the first bit of the storage location. A 1
  in the high-order bit (or left-most bit)
  indicates a negative number and the rest of the
  remaining bits represent the number itself.
• Ex 1 and -1 in an 8-bit word would be
• 0 0 0 0 0 0 0 1 (1)
• 1 0 0 0 0 0 0 1 (-1)

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Signed magnitude addition

• 1 1 1 1 ? carries
• 0 1 0 0 1 1 1 1
• 0 0 1 0 0 0 1 1
• 0 1 1 1 0 0 1 0

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Overflow

• Overflow in signed numbers occurs when the sign
  of the result is incorrect. The sign bit is used
  only for the sign, so we cant carry into it.
• 1 1 1 1 1 ? carries
• 0 1 0 0 1 1 1 1 (79)
• 0 1 1 0 0 0 1 1 (99)
• 0 0 1 1 0 0 1 0 (50)
• 79 99 / 50

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Signed magnitude subtraction

• 0 1 1 2 ? borrows
• 0 1 1 0 0 0 1 1 (99)
• 0 1 0 0 1 1 1 1 (79)
• 0 0 0 1 0 1 0 0 (20)
• 99 79 20

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Ones compliment
Flip the bits for all negative numbers. The last
carry is added to the sum.

• 1 ? 1 1 1 1 1 ? carries
• 0 0 0 1 0 1 1 1 (23)
• 1 1 1 1 0 1 1 0 (-9)
• 0 0 0 0 1 1 0 1
• 1
• 0 0 0 0 1 1 1 0 (14)

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Twos compliment
Flip the bits for all negative numbers. Add 1.
23 00010111 -23 11101000 1 11101001

• 0 0 0 0 1 0 0 1 (9)
• 1 1 1 0 1 0 0 1 (-23)
• 1 1 1 1 0 0 1 0 (-14)

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Section overview

• 2.6 Character Codes
• 2.6.1 Binary-Coded Decimal
• 2.6.2 EBCDIC
• 2.6.3 ASCII
• 2.6.4 Unicode

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Character codes

• Weve gone over how digital computers use the
  binary system to represent and manipulate numeric
  values, but have yet to consider how these
  internal values can be converted to a form that
  is meaningful to humans. This is done through a
  coding system used by the computer and how the
  values are stored and retrieved.

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BCD

• Binary Coded Decimal (BCD) is very common in
  electronics, particularly those that display
  numerical data, such as alarm clocks and
  calculators.
• 4-bit binary form later extended to 6
• 1265 0000 0001 0010 0110 0101 1101

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EBCDIC

• Extended Binary Coded Decimal Interchange Code
  (EBCDIC) used in IBM mainframe and midrange
  computer systems
• 8-bit binary form
• 1265 1111 0001 1111 0010 1111 0110 1101
  0101

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(No Transcript)
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ASCII

• The American Standard Code for Information
  Interchange (ASCII) was created to better
  transmit data between systems.
• Defines codes for 32 control characters, 10
  digits, 52 letters (upper and lower-case), 32
  special characters, and more.

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Unicode

• 16-bit base coding with the capacity to encode
  the majority of characters used in every language
  of the world.
• Unicode also defines an extension mechanism that
  will allow for the coding of an additional
  million characters.
• Default character set of the Java programming
  language.